Fixed Point Logics on Hemimetric Spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F23%3A00574237" target="_blank" >RIV/67985807:_____/23:00574237 - isvavai.cz</a>
Result on the web
<a href="https://dx.doi.org/10.1109/LICS56636.2023.10175784" target="_blank" >https://dx.doi.org/10.1109/LICS56636.2023.10175784</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1109/LICS56636.2023.10175784" target="_blank" >10.1109/LICS56636.2023.10175784</a>

Result language
angličtina
Original language name
Fixed Point Logics on Hemimetric Spaces
Original language description
The μ-calculus can be interpreted over metric spaces and is known to enjoy, among other celebrated properties, variants of the McKinsey-Tarski completeness theorem and of Dawar and Otto's modal characterization theorem. In its topological form, this theorem states that every topological fixed point may be defined in terms of the tangled derivative, a polyadic generalization of Cantor's perfect core. However, these results fail when spaces not satisfying basic separation axioms are considered, in which case the base modal logic is not the well-known K4, but the weaker wK4.In this paper we show how these shortcomings may be overcome. First, we consider semantics over the wider class of hemimetric spaces, and obtain metric completeness results for wK4 and related logics. In this setting, the Dawar-Otto theorem still fails, but we argue that this is due to the tangled derivative not being suitably defined for general application in arbitrary topological spaces. We thus introduce the hybrid tangle, which coincides with the tangled derivative over metric spaces but is better behaved in general. We show that only the hybrid tangle suffices to define simulability of finite structures, a key 'test case' for an expressively complete fragment of the μ-calculus.
Czech name
—
Czech description
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Project
<a href="/en/project/GA22-01137S" target="_blank" >GA22-01137S: Metamathematics of substructural modal logics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Proceedings
ISBN
979-8-3503-3588-0
ISSN
—
e-ISSN
—
Number of pages
13
Pages from-to
190687
Publisher name
IEEE
Place of publication
New York
Event location
Boston
Event date
Jun 26, 2023
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
001036707700049

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